Nonlinear Model Updating Using Recursive and Batch Bayesian Methods

In this paper, an adaptive unscented Kalman filter (AUKF) is developed for state estimation on a tractor-trailer system. For nonlinear systems, the unscented Kalman filter (UKF) is a well-known approach for observer design. Some research has shown the UKF can be more accurate than extended Kalman filter (EKF) with similar computation burden. However, the performance of traditional Kalman filter may deteriorate when process noise changes or sudden disturbance occurs due to the fixed process noise covariance (Q matrix) in the filter. An adaptive gain is calculated to compensate for the mismatch between the actual residual covariance and the deduced value from the filter, ensuring that the sequence of residual is uncorrelated. An estimated Q matrix is referred in the adaptive gain calculation at each sample. Simulation is done in various situations. The positions of trailer are used as measurements. Compared with the standard UKF (SUKF) and another adaptive UKF, the proposed algorithm has better result.

The needle puncture technology is one of the simplest minimally invasive medical procedures. Due to the asymmetry of the needle tip, the lateral force exerted by the tissue causes the tip to deflect and reaches the target position. It is important to maintain the needle tip in a desired plane in 2D control. In the process of puncture, the position is measured and the posture of the needle tip needs to be estimated in real time. Three estimation algorithms for estimating the states of the needle tip are employed in this paper. The first algorithm is adaptive Kalman filter (AKF), which is applied to the statistical properties of the noise is not completely known. The second is unscented Kalman filter (UKF). The last one is the combination of AKF and UKF, called adaptive unscented Kalman filter (AUKF) which combines the advantages of both. It should be noted that AKF is based on the feedback linearization model, but UKF and AUKF are directly based on the nonlinear model. On the base of analysis of three estimation algorithms, we study the control method. In this work, we estimate the states via the three methods and analyze the results. The simulation results of the estimation algorithms and the control method illustrate the differences between the three algorithms.

For the purpose of improving the performance of unscented Kalman filter (UKF) under the condition without accurate system noise statistics, this paper presents a new adaptive UKF based on the maximum likelihood principle. According to the maximum likelihood principle, the estimation of system noise statistics is determined by minimizing the negative of log likelihood function of innovation sequences. Subsequently, the estimated system noise statistics are fed back to the standard UKF to overcome its limitation. The proposed adaptive UKF can enhance the adaptive capability of standard UKF through the online estimation of system noise statistics. The effectiveness and advantage of the proposed algorithm are verified by the numerical simulations and comparison analysis.

For autonomous mobile robots moving in unknown environment, accurate estimation of available power along with the robot power demand for each mission is paramount to successful completion of that mission. Regarding the power consumption, the control unit deals with two tasks simultaneously: 1) it has to monitor the power supply (batteries) state of charge (SoC) constantly. This leads to estimation of robot current available power. Besides, batteries are sensitive to deep discharge or overcharge. The battery SoC is an essential factor in power management of a mobile robot. Accurate estimation of the battery SoC can improve power management, optimize the performance, extend the lifetime, and prevent permanent damage to the batteries. 2) The dynamic characteristics of the terrain the robot traverse requires rapid online modifications in its behaviour. The power required for driving a wheel is an increasing function of its slip ratio. For a wheeled robot moving for driving a wheel is an increasing function of its slip ratio. For a wheeled robot moving on different terrains, slip of the wheels should be checked and compensated for to keep the robot moving with less power consumption. To reduce the power consumption, the target robot moving with less power consumption. To reduce the power consumption, the target of the control system is to keep the slip ratio of the driving wheels around the desired value of the control system is to keep the slip ratio of the driving wheels around the desired value. To fulfill the above mentioned tasks, in this thesis, to increase model validity of lithium-ion battery in various charge/discharge scenarios during the mobile robot operation, the battery capacity fade and internal resistance change are modeled by adding them as state variables to a state space model. Using the output measured data, adaptive unscented Kalman Filter (AUKF) is employed for online model parameters identification of the equivalent circuit model at each sampling time. Subsequently, based on the updated model parameters, SoC estimation is conducted using AUKF. The effectiveness of the proposed method is verified through experiments under different power duties in the lab environment through experiments under different power duties in the lab environment. Better results are obtained both in battery model parameters estimation and the battery SoC estimation in comparison with other Kalman filter extensions. Furthermore, for effective control of the slip ratio, a model-based approach to estimating the longitudinal velocity of the mobile robot is presented. The AUKF is developed to estimate the vehicle longitudinal velocity and the wheel angular velocity using measurements from wheel encoders. Based on the estimated slip ratio, a sliding mode controller is designed for slip control of the uncertain nonlinear dynamical system in the presence of model uncertainties, parameter variations, and disturbances. Experiments are carried out in real time on a four-wheel mobile robot to verify the effectiveness of the estimation algorithm and the controller. It is shown that the controller is able to control the slip ratio of the mobile robot on different terrains while adaptive concept of AUKF leads to better results than the unscented Kalman filter in estimating the vehicle velocity which is difficult to measure in actual practice.

The normal unscented Kalman filter (UKF) suffers from performance degradation and even divergence while mismatch between the noise distribution assumed to be known as a priori by UKF and the true ones in a real system. In this paper, a novel adaptive UKF (AUKF) is developed and applied to nonlinear joint estimation of both time-varying states and parameters. A cost function is built based on the error between the covariance matrices of innovation and their corresponding estimations. An adaptive algorithm is then designed to online update the covariance of the process noise by minimizing the cost function. The updated covariance is further fed back into the normal UKF. As a result of using such an adaptive mechanism, the robustness of conventional UKF is substantially improved with respect to the uncertain and time-varying noise covariance in the real system. To illustrate this mechanism, simulations are conducted on the dynamics of an unmanned helicopter by jointly estimating both the states and model errors. The improvements of the proposed AUKF are demonstrated by comparing the results with and without the adaptive mechanism.

Inherent flaws in the extended Kalman filter (EKF) algorithm were pointed out and unscented Kalman filter (UKF) was put forward as an alternative. Furthermore, a novel adaptive unscented Kalman filter (AUKF) based on innovation was developed. The three data-fusing approaches were analyzed and evaluated in a mathematically rigorous way. Field experiments conducted in lake further demonstrate that AUKF reduces the position error approximately by 65% compared with EKF and by 35% UKF and improves the robust performance.

In the traditional MEMS-INS/GNSS integration, velocity and position are regarded as measurement information. However, it will lead to unobservable of the heading angle, and the heading angle error will be divergent. Eventually, the navigation accuracy will be reduced either. In this paper, a novel approach of heading angle estimation based on Zero-Heading angle-Variation-Constraint (ZHVC) and Sequential-Adaptive Unscented Kalman Filter (SAUKF) algorithms is proposed for avoiding the heading angle unobservability and unstable of the filtering. First, we inspired by the vehicle dynamics and add new information to the original measurement vectors. This new measurement information is the difference of heading angle variations from the MEMS-INS and the theoretical value. Second, we separate the measurement update of Unscented Kalman Filter (UKF) to two parts by sequential method. One is the measurement information of velocity and position, the other one is the heading angle variation. Meanwhile, adaptive UKF only estimate the heading angle variation measurement noise covariance matrix in real-time. The simulation and experiment show that ZHVC can improve the observable degree and accuracy of heading angle than the common method. The SAUKF can estimate heading angle variation measurement noise covariance matrix in real-time. And the filter results are more stable in different motions of the vehicle.

Adaptive unscented Kalman filter for parameter and state estimation of nonlinear high-speed objects

PurposeThis paper aims to develop an adaptive unscented Kalman filter (AUKF) formulation for orientation estimation of aircraft and UAV utilizing low‐cost attitude and heading reference systems (AHRS).Design/methodology/approachA recursive least‐square algorithm with exponential age weighting in time is utilized for estimation of the unknown inputs. The proposed AUKF tunes its measurement covariance to yield optimal performance. Owing to nonlinear nature of the dynamic model as well as the measurement equations, an unscented Kalman filter (UKF) is chosen against the extended Kalman filter, due to its better performance characteristics. The unscented transformation of the UKF is shown to equivalently capture the effect of nonlinearities up to second order without the need for explicit calculations of the Jacobians.FindingsIn most conventional AHRS filters, severe problems can occur once the system suddenly experiences additional acceleration, resulting in erroneous orientation angles. On the contrary in the high dynamic accelerative mode of the new proposed filter the errors would not suddenly increase, since the additional to cruise accelerations are being continuously estimated resulting in substantially more accurate orientation estimation. This feature causes the associated filter errors to gradually increase, in the event of continuous vehicle acceleration, up to a point of zero additional acceleration that subsequently causes a subsidence of the error back to zero.Practical implicationsThe proposed filtering methodology can be implemented for orientation estimation of aircraft and UAV that are equipped with low‐cost AHRSs.Originality/valueTraditional AHRS algorithms utilize the accelerometers output for the computation of roll and pitch angles and magnetometer output for the heading angle. Moreover, these angles are also calculated from the gyroscopes output as well, but with errors that increase with time. Of course for some applications of AHRS system, orientation errors can be damped out with a proportional‐integral controller. In such a case, the filter cut‐off frequency is usually selected experimentally. But, for high accelerating vehicles utilizing AHRS, the system errors can become very large. A possible remedy to this problem could be to use more advanced nonlinear filter algorithms such as the one proposed.

Constrained nonlinear state estimation based on the UKF approach

With the rapid developments in computer technology, the particle filter (PF) is becoming more attractive in navigation applications. However, its large computational burden still limits its widespread use. One approach for reducing the computational burden without degrading the system estimation accuracy is to combine the PF with other filters, i.e., the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). In this paper, the a posteriori estimates from an adaptive unscented Kalman filter (AUKF) are used to specify the PF importance density function for generating particles. Unlike the sequential importance sampling re-sampling (SISR) PF, the re-sampling step is not required in the algorithm, because the filter does not reuse the particles. Hence, the filter computational complexity can be reduced. Besides, the latest measurements are used to improve the proposal distribution for generating particles more intelligently. Simulations are conducted on the basis of a field-collected 3D UAV trajectory. GPS and IMU data are simulated under the assumption that a NovAtel DL-4plus GPS receiver and a Landmark™ 20 MEMS-based IMU are used. Navigation under benign and highly reflective signal environments are considered. Monte Carlo experiments are made. Numerical results show that the AUPF with 100 particles can present improved system estimation accuracy with an affordable computational burden when compared with the AEKF and AUKF algorithms.

The commonly used fixed discrete Kalman filters (DKF) in neural decoders do not generalize well to the actual relationship between neuronal firing rates and movement intention. This is due to the underlying assumption that the neural activity is linearly related to the output state. They also face the issues of requiring large amount of training datasets to achieve a robust model and a degradation of decoding performance over time. In this paper, an adaptive adjustment is made to the conventional unscented Kalman filter (UKF) via intention estimation. This is done by incorporating a history of newly collected state parameters to develop a new set of model parameters. At each time point, a comparative weighted sum of old and new model parameters using matrix squared sums is used to update the neural decoding model parameters. The effectiveness of the resulting adaptive unscented Kalman filter (AUKF) is compared against the discrete Kalman filter and unscented Kalman filter-based algorithms. The results show that the proposed new algorithm provides higher decoding accuracy and stability while requiring less training data.

Ultra-Short Baseline (USBL) systems are susceptible to installation errors that necessitate accurate calibration before deployment. In this paper, we propose an innovative calibration method that does not require time synchronization, enhancing calibration accuracy and mitigating the effects of acoustic array motion. First, we construct a novel installation error model based on the slant range difference to estimate signal sending time. Then, we designed an improved filtering algorithm—variational Bayesian unscented Kalman filter-range (VBUKF-r). In VBUKFr, to address challenges related to unknown and time-varying measurement noise covariance matrix (MNCM), we integrate variational Bayesian methods with the unscented Kalman filter (UKF) and enhance the accuracy of MNCM estimation by analyzing the relationship between ranging noise and distance. Furthermore, we utilize matrix diagonalization instead of Cholesky decomposition to resolve computational issues associated with non-positive definite state covariance matrixs. Finally, we propose a K-means clustering iterative optimization strategy for VBUKF-r to mitigate the influence of initial measurement vectors on parameter estimation. Simulation analysis and sea trials demonstrate that our algorithm significantly outperforms existing methods.

State of Charge (SOC) estimation plays a crucial role in managing the performance and longevity of electric vehicle (EV) batteries. Various estimation techniques, including various Kalman Filters (KF), have been employed for this purpose. The mathematical process and limits of different KF family algorithms are analysed. In this study, an impact of nonlinear KF parameters on SOC estimation accuracy for EV batteries is analyzed. Specifically, the performance of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF) is examined. EKF is most preferred for SOC estimation whereas introducing sigma points in UKF is the basic difference between EKF and UKF. In comparison to EKF and UKF, PF is more flexible since it applies to nonlinear systems with non-Gaussian distributions. Utilising a sequence of noisy measurements, KF is a recursive method that approximates the state of a dynamic system. It requires accurate parameters such as process noise covariance (Q) and measurement noise covariance (R) to work effectively. In this work, the effect of these parameters on state of charge estimation using nonlinear KFs has been analysed under different settings of noise covariance matrices. Tuning these parameters is essential for optimizing the performance of the KF and ensuring accurate and reliable state estimation in real-world applications. To find parameter values that provide the best balance between accuracy, robustness, and computational efficiency, the tuning process involves experimentation, simulation, and validation using real-world data. According to the results observed, the filter parameters such as three diagonal elements of Q are selected as 2e-8, 0.005, 0.003 and R as 2e-6. By evaluating the state estimation accuracy under different driving scenarios, robustness and sensitivity of filtering technique in estimating SOC for EV batteries has been studied. This analysis contributes to the optimization of SOC estimation algorithms, enhancing the reliability and efficiency of EV battery management systems.

A residual based adaptive unscented Kalman filter for fault recovery in attitude determination system of microsatellites